I was considering Ginnie Springs and Blue Grotto as backups if we lose a day or two of diving but that's over 4 hours from where we will be staying in West Palm. Are there closer inland dive sites?
Paradise is a little closer, there is also Blue Springs up near Daytona.
But if the weather is looking bad for a couple of days I would spend two days (with driving) going to Paradise, Ginnie, and Devil's Den. Those are probably the best ones you can go to without any sort of overhead cert.